Khan.scratchpad.disable(); For every level Vanessa completes in her favorite game, she earns $780$ points. Vanessa already has $300$ points in the game and wants to end up with at least $2710$ points before she goes to bed. What is the minimum number of complete levels that Vanessa needs to complete to reach her goal?
Answer: To solve this, let's set up an expression to show how many points Vanessa will have after each level. Number of points $=$ $ $ Levels completed $\times$ Points per level $+$ Starting points Since Vanessa wants to have at least $2710$ points before going to bed, we can set up an inequality. Number of points $\geq 2710$ Levels completed $\times$ Points per level $+$ Starting points $\geq 2710$ We are solving for the number of levels to be completed, so let the number of levels be represented by the variable $x$ We can now plug in: $x \cdot 780 + 300 \geq 2710$ $ x \cdot 780 \geq 2710 - 300 $ $ x \cdot 780 \geq 2410 $ $x \geq \dfrac{2410}{780} \approx 3.09$ Since Vanessa won't get points unless she completes the entire level, we round $3.09$ up to $4$ Vanessa must complete at least 4 levels.